Permutations and Combinations 2 Question 22
22. 7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’s relatives?
Show Answer
Answer:
Correct Answer: 22. (485)
Solution:
- The possible cases are
Case I A man invites 3 ladies and women invites 3 gentlemen.
Number of ways
Case II A man invites (2 ladies, 1 gentleman) and women invites (2 gentlemen, 1 lady).
Number of ways
Case III A man invites (1 lady, 2 gentlemen) and women invites (2 ladies, 1 gentleman).
Number of ways
Case IV A man invites (3 gentlemen) and women invites (3 ladies).
Number of ways
